Theoretically the value of elastic constants for isotropic materials can be determined with the knowledge of any two elastic constants, from either of the following equation (1).
ν=1/2-
E/6
B,
E=2
G(1+ν) (1) when,
E: Young′s modulus,
E=σ/ε, σ: Stress, ε: Strain,
G: Shear modulus,
B: Bulk modulus, ν: Poisson′s ratio.
The rubber deformation takes place without change in volumes so that obtained equation (2).
ν=0.5,
E=3
G (2)
Bartenev shows equation (3) when large deformation of the rubber.
σ=
E(1-λ
-1), λ=1+ε (3)
But from (2) and (3) obtained equation (4) σ=3
G(1-λ
-1) did not fit for experimental data by Treloar stress-strain curve. σ=
G(λ-λ
-2) also famous equation but the experiment failed of success at tensile side to Treloar data.
My idea is defined rubber-like Poisson′s ratio (ν
R) and rubber-like Young′s modulus (E
R), (ν
R)=ε′/ε =(1-1/√<λ>)/(λ-1), (
ER)=2
G(1+(ν
R))…(5), and (
ER) relation input Bartenev equation (3), gained σ-λ formula (6), σ=2
G(1-λ
-1.5).
This equation (6) shows very close agreement to the Treloar tensile and compression data in the pragmatic strain region from about 2>λ>0.5.
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